Absolutely, let's solve the problem step-by-step.
### Given Data:
- Initial Investment: [tex]\( \$13,000 \)[/tex]
- Distribution: [tex]\( \$260 \)[/tex]
- Final Value: [tex]\( \$11,400 \)[/tex]
### a) Income Yield
The income yield is calculated as the income (distribution) received over the period divided by the initial investment, expressed as a percentage:
[tex]\[ \text{Income Yield} = \left( \frac{\text{Distribution}}{\text{Initial Investment}} \right) \times 100 \][/tex]
Substitute the given values:
[tex]\[ \text{Income Yield} = \left( \frac{260}{13000} \right) \times 100 \][/tex]
Calculate the fraction:
[tex]\[ \frac{260}{13000} = 0.02 \][/tex]
Convert the fraction to a percentage:
[tex]\[ 0.02 \times 100 = 2.00\% \][/tex]
So, the Income Yield is 2.00%.
### b) Capital Gain Yield
The capital gain yield is calculated as the change (gain or loss) in value of the investment over the period divided by the initial investment, also expressed as a percentage:
[tex]\[ \text{Capital Gain Yield} = \left( \frac{\text{Final Value} - \text{Initial Investment}}{\text{Initial Investment}} \right) \times 100 \][/tex]
Substitute the given values:
[tex]\[ \text{Capital Gain Yield} = \left( \frac{11400 - 13000}{13000} \right) \times 100 \][/tex]
Calculate the numerator:
[tex]\[ 11400 - 13000 = -1600 \][/tex]
Next, calculate the fraction:
[tex]\[ \frac{-1600}{13000} = -0.1231 \][/tex]
Convert the fraction to a percentage:
[tex]\[ -0.1231 \times 100 = -12.31\% \][/tex]
So, the Capital Gain Yield is -12.31%.
### c) Rate of Total Return
The rate of total return is the sum of the income yield and the capital gain yield:
[tex]\[ \text{Rate of Total Return} = \text{Income Yield} + \text{Capital Gain Yield} \][/tex]
Substitute the calculated values:
[tex]\[ \text{Rate of Total Return} = 2.00\% + (-12.31\%) \][/tex]
Calculate the sum:
[tex]\[ 2.00\% - 12.31\% = -10.31\% \][/tex]
So, the Rate of Total Return is -10.31%.
### Summary:
- Income Yield: [tex]\( 2.00\% \)[/tex]
- Capital Gain Yield: [tex]\( -12.31\% \)[/tex]
- Rate of Total Return: [tex]\( -10.31\% \)[/tex]
These calculations show the different components of your investment's performance over the last year.
